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Lesson_1.2_Homework_Solution

# Lesson_1.2_Homework_Solution - Lesson 1.2 Homework...

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Lesson 1.2 Homework Solutions 1. A car traveling at 36 kmh -1 accelerates to 72 kmh -1 in 5.0 s. What is the acceleration of the car? v o = 36 kmh -1 = 10 ms -1 , v f = 72 kmh -1 = 20 ms -1 , t = 5.0 s -1 2 -1 20 ms 10 ms 5.0 s 2 f o v v a t ms - - = - = = 2. A car traveling at 90 kmh -1 is brought to rest in 15 s. What is the acceleration of the car? v o = 0 kmh -1 , v f = 90 kmh -1 = 25 ms -1 , t = 15 s 1 2 - -1 0 ms 25 ms 15 s 1.7 f o ms v v a t - = - - - = = 3. A car initially at rest at the top of a hill rolls down the hill with a uniform acceleration of 5.0 ms -2 . How long will it take the car to roll down a distance of 150 m? v o = 0 kmh -1 , a = 5 ms -2 , Distance x = 150 m x = v o t + ½ at 2 150 = 0 + ½ (5.0 ms -2 ) t 2 = 2.5t 2 t 2 = 60 s 2 t = 7.75 s 4. Sketch the graphs of (a) velocity v versus time t and (b) displacement y versus time t for a freely falling object. (a) The initial velocity of a freely falling object is zero. With time the velocity increases in the negative direction. 0 1 2 3 4 5 10 20 time, s velocity, m/s -10 -20 -30 -40

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(b) The initial position of the object is y o . The position decreases with time. Each second the decrease is greater than the previous second. 0 1 2 3 4 5 10 20 time, s position (m) 30 40 5. 2 4 6 -2 -4 -6 6 2 4 8 10 12 14 v, m/s t, s A B C D E F The figure above shows how the velocity of a moving object changes with time. (i) What is the acceleration of the object from A to B? (ii) What is the acceleration of the object from C to D? (iii) What is the acceleration of the object from D to E? (iv) What are the times when the instantaneous velocities are zero. (v) What is the displacement of the object from t = 0 to t = 6 s? (vi) What is the displacement of the object from t = 0 to t = 10 s? (vii) What is the displacement of the object for the entire trip? (i) Acceleration from A to B is the slope of the line AB = 5/6 = 0.83 m.s -2 (ii) Acceleration from C to D is the slope of the line CD = 5/2 = 2.5 m.s -2
(iii) Acceleration from D to E = 0 (iv) Instantaneous velocities are zero where the graph crosses the t- axis. This corresponds to t = 0, 7.5 s, 10 s and 15 s. (v) Displacement from t = 0 to t = 6 is the area under the graph AB = (1/2) × 6 × 5 = 15 m (vi) 2 4 6 -2 -4 -6 6 2 4 8 10 12 14 v, m/s t, s A B C D E F The displacement from t = 0 to t = 10 s is represented by the shaded area in the figure above. Notice here that the green area

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Lesson_1.2_Homework_Solution - Lesson 1.2 Homework...

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